Shape theory and asymptotic morphisms for \(C^*\)-algebras

DOI10.1215/S0012-7094-94-07327-4zbMath0847.46028OpenAlexW1991854441MaRDI QIDQ1325147

Marius Dǎdǎrlat

Publication date: 8 October 1996

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-94-07327-4

zbMATH Keywords

topological invariantsisomorphism classshape invariantseparable \(C^*\)-algebrasasymptotic homotopy categoryConnes-Higson categoryhomotopy invariant functor on separable \(C^*\)-algebras

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) (46M20) General theory of (C^*)-algebras (46L05)

Related Items (13)

A note on asymptotic homomorphisms ⋮ Approximately unitarily equivalent morphisms and inductive limit \(C^*\)- algebras ⋮ Quasidiagonal morphisms and homotopy ⋮ Classification of \(C^*\)-algebras of real rank zero and unsuspended \(E\)-equivalence types ⋮ Classifying \(C^*\)-algebras via ordered, mod-\(p\) \(K\)-theory ⋮ The point in weak semiprojectivity and AANR compacta ⋮ Subalgebras of finite codimension in semiprojective 𝐶*-algebras ⋮ E-theory for \(C^*\)-algebras over topological spaces ⋮ Noncommutative geodesics and the KSGNS construction ⋮ Homotopical algebra for \(C^\ast\)-algebras ⋮ Inductive limits of semiprojective \(C^{\ast}\)-algebras ⋮ Deformations of nilpotent groups and homotopy symmetric \(C^*\)-algebras ⋮ Shape theory

Cites Work

• Homotopy after tensoring with uniformly hyperfinite \(C^*\)-algebras
• The Künneth theorem and the universal coefficient theorem for Kasparov's generalized K-functor
• \(C^ \ast\)-algebras generated by stable relations
• Cech and Steenrod homotopy theories with applications to geometric topology
• On the asymptotic homotopy type of inductive limit \(C^*\)-algebras
• \(K\)-homology, asymptotic representations, and unsuspended \(E\)-theory
• Categories of fractions and excision in KK-theory
• THE OPERATORK-FUNCTOR AND EXTENSIONS OFC*-ALGEBRAS
• Shape theory for $C^*$-algebras.
• An exact sequence from the nth to the (n-1)-st fundamental group
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